Bender bar modal shaping

ABSTRACT

An acoustic transducer, such as a bender bar, having ferroelectric actuation elements that are designed to optimize a predetermined deflection mode shape. The acoustic transducers may include one or more rounded modally shaped actuation elements or weighted actuation elements. Modal shaping of the actuation elements allows for specific targeting of modes which most efficiently radiate acoustic energy.

The present application is a U.S. National Stage patent application of International Patent Application No. PCT/US2014/017760, filed on Feb. 21, 2014, the benefit of which is claimed and the disclosure of which is incorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to downhole acoustic tools and, more specifically, to a downhole acoustic tool having an actuation element designed to match certain deflection mode shapes of the acoustic tool.

BACKGROUND

Acoustic well logging is a well-developed art, and details of acoustic logging tools and techniques are set forth in A. Kurkjian, et al., “Slowness Estimation from Sonic Logging Waveforms”, Geoexploration, Vol. 277, pp. 215-256 (1991); C. F. Morris et al., “A New Sonic Array Tool for Full Waveform Logging,” SPE-13285, Society of Petroleum Engineers (1984); A. R. Harrison et al., “Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole and Dipole Source . . . ” SPE 20557, pp. 267-282 (September 1990); and C. V. Kimball and T. L. Marzetta, “Semblance Processing of Borehole Acoustic Array Data”, Geophysics, Vol. 49, pp. 274-281 (March 1984). An example of an acoustic logging tool is provided in U.S. Pat. No. 6,661,737 entitled “ACOUSTIC LOGGING TOOL HAVING PROGRAMMABLE SOURCE WAVEFORMS,” owned by the Assignee of the present disclosure, Halliburton Energy Services, Inc. of Houston, Tex.

An acoustic logging tool typically includes an acoustic source (transmitter), and a set of receivers that are spaced several inches or feet apart. An acoustic signal is transmitted by the acoustic source and received at the receivers of the borehole tool which are spaced apart from the acoustic source. Measurements are repeated every few inches as the tool passes along the borehole. The acoustic signal from the source travels through the formation adjacent the borehole to the receiver array, and the arrival times and perhaps other characteristics of the receiver responses are recorded.

Typically, compressional wave (“P-wave”), shear wave (“S-wave”), and Stoneley wave arrivals and waveforms are detected by the receivers and are processed. The processing of the data is often performed on the surface, although it may also be performed real time in the tool itself. Regardless, the information that is recorded is typically used to determine formation characteristics, such as formation slowness (the inverse of acoustic speed) and anisotropy, from which pore pressure, porosity, and other formation property determinations can be made. With some tools, the acoustic signals may even be used to image the formation.

Acoustic logging tools are used for both wireline logging and logging while drilling applications. In wireline logging, a probe, or “sonde”, housing multiple logging tools is lowered into the borehole after some or all of the well has been drilled. The sonde is attached to a conductive wireline that carries power from the surface to the tools in the sonde, and that carries telemetry information to the surface. The sonde may be transported through the borehole by the wireline, or a separate transport mechanism may be provided. For example, in “pipe-conveyed” logging, the sonde is mounted on a tubing string. The rigidity of the tubing string allows the sonde to be transported through highly deviated and horizontal boreholes.

One problem with obtaining downhole measurements via wireline is that the drilling assembly must be removed or “tripped” from the drilled borehole before the desired borehole information can be obtained. This can be both time-consuming and extremely costly, especially in situations where a substantial portion of the well has been drilled. In this situation, thousands of feet of tubing may need to be removed and stacked on the platform (if offshore). Typically, drilling rigs are rented by the day at a substantial cost. Consequently, the cost of drilling a well is directly proportional to the time required to complete the drilling process. Removing thousands of feet of tubing to insert a wireline logging tool can be an expensive proposition.

As a result, there is a strong incentive to minimize the number of wireline logging trips. One way to do this involves collection of data during the drilling process. Designs for measuring conditions downhole, including the movement and location of the drilling assembly contemporaneously with the drilling of the well, have come to be known as “measurement-while-drilling” techniques, or “MWD”. Similar techniques, concentrating more on the measurement of formation parameters, commonly have been referred to as “logging while drilling” techniques, or “LWD”. While distinctions between MWD and LWD may exist, the terms MWD and LWD often are used interchangeably. For the purposes of this disclosure, the term LWD will be used with the understanding that this term encompasses both the collection of formation parameters and the collection of information relating to the movement and position of the drilling assembly.

LWD tools are generally located as close to the drill bit as possible, so as to minimize the delay between reaching a formation and measuring its properties. When implemented as LWD tools, acoustic logging tools must overcome a number of obstacles to perform successfully. These obstacles include drilling noise, and acoustic properties of the thick tool body.

Bender bars are utilized in acoustic logging tools to detect and/or generate acoustic vibrations or seismic waves. Bender bars can be utilized in both the transmitter portion and the receiver portion of the acoustic logging tool. However, current bender bars have difficulties with low frequency responses, resulting in difficulties in producing high quality logs for large hole and soft formation applications. Additionally, other challenges faced by traditional bender bars also include the generation of larger and more consistent acoustic with lower voltage requirements, while also maintaining high modal purity. Moreover, traditional bender bars have utilized square piezoelectric ceramic actuators mounted on a clamped-clamped beam. However, this design fails to make the most efficient use of the actuator.

Accordingly, there is a need in the art for an improved bender bar that overcomes these and other limitations.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrate a basic bender bar;

FIGS. 2A, 2B, 2C, and 2D illustrate embodiments of a stacked bender bar according to certain illustrative embodiments of the present disclosure;

FIG. 3 illustrates a schematic for driving bipolar elements of stacked bender bars such as those illustrated in FIGS. 2A, 2B, 2C, and 2D;

FIGS. 4A, 4B, and 4C illustrate the results of driving the bipolar elements of an illustrative stacked bender bar under different impulse characteristics;

FIG. 5 illustrates a particular example of a basic bender bar as shown in FIG. 1;

FIGS. 6A, 6B, and 6C illustrate three symmetrical harmonic modes for the illustrative bender bar illustrated in FIG. 5;

FIG. 7 illustrates the harmonic displacement of the center point of the illustrative bender bar illustrated in FIG. 5;

FIG. 8 illustrates a particular example of a stacked bender bar such as that illustrated in FIGS. 2A and 2B according to certain illustrative embodiments of the present disclosure;

FIGS. 9A, 9B, and 9C illustrate three symmetric modes of the stacked bender bar illustrated in FIG. 8;

FIG. 10 illustrates a comparison of the harmonic displacement in the Z direction of the stacked bender bar illustrated in FIG. 8 with that of the bender bar illustrated in FIG. 5;

FIGS. 11A and 11B illustrate a bender bar according to certain illustrative embodiments of the present disclosure;

FIG. 11C illustrates a particular example of the bender bar illustrated in FIGS. 11A and 11B;

FIGS. 12A, 12B, and 12C illustrate three symmetric mode shapes for the bender bar illustrated in FIG. 11C;

FIG. 13 illustrates a comparison of the harmonic displacement in the Z direction of the bender bar illustrated in FIG. 11C with that of the bender bar illustrated in FIG. 5;

FIGS. 14A, 14B, 14C, and 14D illustrate a stacked bender bar according to certain illustrative embodiments of the present disclosure;

FIG. 15 illustrates a particular example of the bender bar illustrated in FIGS. 14A and 14B;

FIGS. 16A, 16B, and 16C illustrate the three symmetric mode of a stacked bender bar illustrated in FIG. 15;

FIG. 17 illustrates a comparison of the harmonic displacement in the Z direction of the bender bar illustrated in FIG. 15 with that of the bender bar illustrated in FIG. 5;

FIG. 18 illustrates a narrow band pulse for driving the PZT elements;

FIG. 19 illustrates the effects of the multiple driving pulse shapes in different PZT elements; and

FIGS. 20A and 20B are sectional and top-down views, respectively, of another illustrative embodiment of the present disclosure wherein an acoustic tool (bender bar, for example) includes a ferroelectric actuator that is designed to optimize a specific predetermined deflection mode shape of the tool;

FIG. 21 plots a frequency response comparison of a finite element analysis simulation of a modally shaped transducer (solid line) with strain relief versus a conventional square actuator (dashed line), according to an illustrative embodiment of the present disclosure;

FIGS. 22A-B illustrate an alternative embodiment of a transducer that utilizes weighted ferroelectric actuation elements to achieve modal shaping;

FIGS. 23A-D illustrate rounded modally shaped transducers at rest and in the third mode of vibration, according to certain illustrative embodiments of the present disclosure; and

FIGS. 24A-B illustrate acoustic transducers utilized in a drilling and wireline application, respectively, according to illustrative embodiments of the present disclosure.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Illustrative embodiments and related methodologies of the present disclosure are described below as they might be employed in an acoustic tool (bender bar, for example) having improved construction, operation and control. In the interest of clarity, not all features of an actual implementation or methodology are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. Further aspects and advantages of the various embodiments and related methodologies of the disclosure will become apparent from consideration of the following description and drawings.

FIGS. 1A and 1B illustrate a bender bar transducer 100. As shown in the cross-sectional view of FIG. 1A, transducer 100 includes ferrelectric elements 104 a and 104 b mounted on an inert element 102. Inert element 102 may be, for example, aluminum or some other suitable non-ferroelectric element. As shown in FIG. 1B, ferroelectric elements 104 a and 104 b are slabs of mater that are mounted on inert element 102. As shown in FIG. 1A, the ferroelectric elements of ferroelectric elements 104 a and 104 b are electrically coupled to electronics 106. Electronics 106 may include driver circuits or receiver elements such as that illustrated, for example, in U.S. Pat. No. 6,661,737. As described therein, this illustrative embodiment of transducer 100 provides a bi-polar acoustic wave as it is driven by electronics 106.

FIGS. 2A, 2B, 2C, and 2D illustrate certain illustrative embodiments of a bender bar transducer 200 according to aspects of the present disclosure. As shown in FIG. 2A, bender bar transducer 200 includes an inert element 210. Multiple ferroelectric slabs are mounted in layers on each side of inert element 210 to form a stacked bender bar. As shown in the particular example illustrated in FIG. 2A, ferroelectric elements 202 a and 202 b are mounted on opposite sides of inert element 210. Ferroelectric element 204 a is mounted on ferroelectric element 202 a and ferroelectric element 204 b is mounted on ferroelectric element 202 b. Ferroelectric element 206 a is mounted on ferroelectric element 204 a and ferroelectric element 206 b is mounted on ferroelectric element 204 b. Ferroelectric element 208 a is mounted on ferroelectric element 206 a and ferroelectric element 208 b is mounted on ferroelectric element 206 b.

FIGS. 2A, 2B, 2C and 2D specifically illustrate an example embodiment with three pairs of stacked ferroelectric elements—ferroelectric elements 204 a and 204 b, 206 a and 206 b, and 208 a and 208 b. Alternatively, any number of pairs of ferroelectric elements can be utilized, as the example illustrated in FIGS. 2A, 2B, 2C, and 2D are illustrative only.

Inert element 210 can be any element that is not piezoelectric in nature. For example, inert element 120 can be Al, brass, titanium, or any metal or alloy. Ferroelectric elements 202 a, 202 b, 204 a, 204 b, 206 a, 206 b, 208 a, and 208 b can be any piezoelectric elements, for example lead zirconate titanate (PZT), barium titanate (BaTiO₃), Gallium orthophosphate (GaPO₄), Tourmaline, Quartz, or other ferroelectric material. The term ferroelectric material is used to refer to any ferroelectric or relaxor ferroelectric material that exhibits a coupling between voltage and mechanical motion. The piezoelectric material can be a ceramic or a polymer. Without limitation, the piezoelectric material can be described as an electrostrictor, a piezoceramic, piezopolymer, magnetostrictor, or a shape memory ceramic. As shown in FIG. 2A, pairs of ferroelectric elements—ferroelectric elements 202 a, 202 b; 204 a, 204 b; 206 a, 206 b, and 208 a, 208 b—are stacked. Each layer of piezoelectric element in the stacking can have different thicknesses and can have differing widths and lengths. For purposes of this disclosure, thickness refers to the dimension perpendicular to the largest planar surface of inert element 210, the surfaces on which ferroelectric element 202 a and 202 b are mounted, and the length and width refer to dimensions in the plane of inert element 210. The various layers of ferroelectric element are differently sized and may be of different types of ferroelectric elements in order to better control the response of transducer 200.

FIG. 2B illustrates an illustrative stacking arrangement of transducer 200. As shown in FIG. 2B, each of ferroelectric elements 202 a, 204 a, 206 a, and 208 a are rectangular bars with each of them of different lengths but similar widths. As shown in FIG. 2B, ferroelectric element 202 a is mounted to inert element 210 in a symmetric fashion. Ferroelectric element 204 a is symmetrically mounted on ferroelectric element 202 a. Ferroelectric element 206 a is symmetrically mounted on ferroelectric element 204 a, ferroelectric element 208 a is symmetrically mounted on ferroelectric element 206 a, while ferroelectric elements 202 b, 204 b, 206 b, and 208 b are similarly stacked on the opposite side of inert element 210, as is shown in FIG. 2A.

FIG. 2C illustrates another example of a stacking arrangement of transducer 200. As shown in FIG. 2C, each of ferroelectric elements 202 a, 204 a, 206 a, and 208 a are rectangular bars having differing dimensions in both length and width. As shown in FIG. 2C, ferroelectric element 202 a is symmetrically mounted on inert element 210. Ferroelectric element 204 a is symmetrically mounted on ferroelectric element 202 a; ferroelectric element 206 a is symmetrically mounted on ferroelectric element 204 a; and ferroelectric element 208 a is symmetrically mounted on ferroelectric element 206 a. Ferroelectric elements 202 b, 204 b, 206 b, and 208 b are the same sizes as ferroelectric elements 202 a, 204 a, 206 a, and 208 a and are similarly arranged on the opposite side of inert element 210.

FIG. 2D illustrates another example of a stacking arrangement of transducer 200. As shown in FIG. 2D, only ferroelectric element 202 a is rectangular in shape. Ferroelectric elements 204 a, 206 a, and 208 a are elliptical, or disc-shaped, slabs in shape, with the minor and major axis of the ellipse corresponding to width and length directions, respectively. As shown in FIG. 2D, each of the elliptical layers 204 a, 206 a, and 208 a are of different sizes. Further, ferroelectric element 202 a is symmetrically mounted on inert element 210. Ferroelectric element 204 a is symmetrically mounted on ferroelectric element 202 a; ferroelectric element 206 a is symmetrically mounted on ferroelectric element 204 a; and ferroelectric element 208 a is symmetrically mounted on ferroelectric element 206 a. Ferroelectric elements 202 b, 204 b, 206 b, and 208 b are the same sizes and shapes as ferroelectric elements 202 a, 204 a, 206 a, and 208 a and similarly arranged on the opposite side of inert element 210.

The stacked ferroelectric element pairs 204 a and 204 b, 206 a and 206 b, and 208 a and 208 b can provide mass loading to the dipole at the center of maximum bending. This mass loading forces the frequency response of transducer 200 toward lower frequencies and lowers the quality factor Q. A similar effect was attempted and disclosed in U.S. Pat. No. 7,692,363, however the mass loading proposed in that disclosure was not capable of being driven.

In accordance with certain illustrative embodiments of the present disclosure, each of ferroelectric element pairs 202 a and 202 b, 204 a and 204 b, 206 a and 206 b, and 208 a and 208 b can be independently driven with controlled pulses to enhance further the low frequency response of transducer 200. FIG. 3 illustrates a schematic of a driver 300 for driving each bipolar element, a bipolar element being formed by each of the ferroelectric element pairs. In some embodiments, individual (unipolar) elements (formed by individual ones of ferroelectric elements) can be driven separately by driver circuit 300 to achieve asymmetric acoustic radiation.

The embodiment of driver circuit 300 illustrated in FIG. 3 is a bipolar driver where individual ferroelectric pairs (ferroelectric element 202 a and 202 b; 204 a and 204 b; 206 a and 206 b; and 208 a and 208 b) are driven simultaneously and synchronously. As shown in FIG. 3, driver 300 includes a controller 302 that controls pulse generators 304, 306, 308, and 310. Pulse generator 304 is coupled through a driver 312 to produce signal S1, which is coupled to drive ferroelectric element 202 a and 202 b. Pulse generator 306 is coupled through a driver 314 to produce signal S2, which is coupled to drive ferroelectric element 204 a and 204 b. Pulse generator 308 is coupled through a driver 316 to produce signal S3, which is coupled to drive ferroelectric element 206 a and 206 b. Pulse generator 310 is coupled through a driver 318 to produce signal S4, which is coupled to drive ferroelectric element 208 a and 208 b.

In some embodiments of the present disclosure, output signals produced by transducer 200 can be detected by sensors 320. Signals from sensors 320 can be input to controller 302, which can then adjust the signals S1, S2, S3, and S4 supplied to transducer 200 to provide desirable results. One such desirable result can be, for example, enhancing the dipole nature of transducer 200 and the suppression of other modes of vibration.

FIGS. 4A, 4B, and 4C illustrate the results of different driving pulses for S1, S2, S3, and S4. As shown in FIG. 4A, signals S1, S2, S3, and S4 that are in phase with one another will add to the effect and produce a large signal. FIG. 4B illustrates the effects of shifting signals S1, S2, S3, and S4 in phase with respect to one another. As shown in FIG. 4B, the resulting output signal is broader. As shown in FIG. 4C, as the phase between the impulses S1, S2, S3, and S4 are increased, the resulting output signal becomes more diffuse.

Some embodiments of transducer 200 can experience larger displacements due to the stacking of ferroelectric elements, resulting in mass loading as well as the ability to drive multiple pairs of ferroelectric elements. The overall thickness of the stacking and resulting mass loading can also result in a lower frequency response and a lower Q. Controlling the pulses to each of the ferroelectric element pairs in frequency, amplitude, and shape can produce much lower or higher frequency responses with larger displacements. The displacements, as illustrated above, can be controlled by adjusting the phasing between individual signals supplied to the ferroelectric element pairs. In some embodiments, controlling pulse signals to individual pairs of ferroelectric elements can also be used to equalize the dipole displacement at both sides and thereby minimize Stoneley mode generation (generation of waves that travel along the wellbore). This effectively enhances a pure dipole signal output signal and increases the dipole signal-to-noise (S/N). In some embodiments of the present disclosure, numerous adaptive pulse controls produced by monitoring the output signals can be added to improve the dipole quality of the output signals produced by transducer 200.

Performance of a basic bender bar 100 with an embodiment of a stacked bender bar 200 were modeled and compared with utilizing a WaveSonic™ (Halliburton Acousitc logging tool) dipole source, which may include transmitter driving circuit board Part No. 101507949 and Wireline Tool part no 101378058 manufactured by Halliburton Energy Services, Inc. The performance of the bender bar was modeled and analyzed utilizing a multiphysics modeling package by COMSOL, Inc. (COMSOL) and a second package by Simulia, Inc., called the ABAQUS software packages (ABAQUS). Both COMSOL and ABAQUS are finite element multi-physics modeling packages.

It was found that the COMSOL package is not stable and could not produce any dynamic response. As a result, only ABAQUS modeling results are presented in this disclosure. The software package ABAQUS is capable of performing several kinds of analysis to give insight to the performance of a bender bar. These analyses include Natural Frequency Extraction, Direct-Solution Steady-State Dynamic Analysis, and Implicit Dynamic Analysis using Direct Integration. The response was modeled without loading (no surrounding medium). The proposed concepts of this discloser are verifiable utilizing this software and the results are provided below.

FIG. 5 illustrates a particular example of bender bar 100 that is utilized for analysis as discussed above. In this analysis, bender bar 100 is a PZT bender bar. Specifically, inert element 102 is a brass plate of thickness 0.125 inch, length 7.7 inch, and width 1.1 inch. Ferroelectric elements 104 a and 104 b are PZT crystal (C5400 or PZT-4 that may be purchased, for example, from Channel Industries or Piezo Technologies). Each of Ferroelectric elements 104 a and 104 b has a thickness of 0.125 inch, length of 4.0 inch, and width of 1.0 inch. Ferroelectric elements 104 a and 104 b are bonded to inert element 102, for example, with epoxy or a resin.

Natural Frequency Extraction (Modal analysis) is performed utilizing the particular example of bender bar 100 illustrated in FIG. 5 to calculate the natural frequencies and the corresponding mode shapes of bender bar 100. The ABAQUS model utilizes an eigenvalue analysis to find the various modes and mode frequencies. For the WaveSonic™ bender bar model shown in FIG. 5, 14 vibrational modes between 0 and 10 kHz where found. Those modes are listed in Table 1. The more important modes are the symmetric modes, which for bender bar 100 of FIG. 5 are listed as mode 1 at 383.6 Hz, mode 5 at 2622.8 Hz, and mode 9 at 5887.7 Hz, which are themselves illustrated in FIGS. 6A, 6B, and 6C, respectively. The harmonic displacement of the center point is illustrated in FIG. 7 as a function of frequency.

TABLE 1 Mode 1 2 3 4 5 6 7 Freq 383.6 956.5 1009.2 1762.6 2622.8 4709 4717 (Hz) Mode 8 9 10 11 12 13 14 Freq 5306.4 5887.7 6290.7 6846.6 7856.1 8217.4 9330 (Hz)

Bender bar 100 can have several types of mode shapes. The various types of bending include, for example, twisting, swinging sidewise, and swinging lengthwise. Among these, only certain symmetric bending modes provide substantial pressure when bender bar 100 is coupled to an acoustic medium. FIGS. 6A, 6B, and 6C show symmetric bending modes corresponding to the modes at 363.6 Hz, 2622.8 Hz, and 5887.7 Hz, respectively. FIGS. 6A, 6B, and 6C are not to scale and are provided to emphasize the mode shapes only. FIG. 6A shows a mode having no internal nodes. FIG. 6B illustrates a mode having two internal nodes. FIG. 6C shows a mode having 4 internal nodes.

FIG. 7 shows the harmonic displacement in Z-direction of the center point of the bar. In this model, illustrated in FIG. 7, there is no loading (i.e., no surrounding medium). FIG. 7 illustrates peaks 702, 704, and 706, corresponding to mode 1, mode 5, and mode 9 of Table 1, respectively. The results illustrated in FIG. 7 are based on a theoretical model of the ABAQUS system. FIG. 7 illustrates that peaks 702, 704, and 706 are observed at the symmetrical modes 1, 5, and 9 shown in FIGS. 6A, 6B, and 6C, respectively.

FIG. 8 illustrates a particular example of a stacked bender bar 200 on which frequency calculations can be performed. In the embodiment shown in FIG. 8, stacked bender bar 200 includes inert element 210, ferroelectric elements 202 a and 202 b and ferroelectric elements 204 a and 204 b. Inert element 210 and ferroelectric elements 202 a and 202 b are the same elements and dimensions as inert element 102 and ferroelectric elements 104 a and 104 b illustrated in FIG. 5. In other words, inert element 210 is a brass plate of thickness 0.125 inch, length 7.7 inch, and width 1.1 inch. Ferroelectric elements 202 a and 202 b are PZT crystal (C5400 or PZT-4, which may be purchased, for example, from Channel Industries or Piezo Technologies). Each of Ferroelectric elements 202 a and 202 b has a thickness of 0.125 inch, length of 4.0 inch, and width of 1.0 inch. Ferroelectric elements 202 a and 202 b are bonded to inert element 210 with an epoxy or resin. Ferroelectric elements 204 a and 204 b are half sized of ferroelectric elements 202 a and 202 b, having thickness of 0.125 inch, length of 2.0 inch, and width of 1.0 inch. Ferroelectric elements 204 a and 204 b are bonded to ferroelectric elements 202 a and 202 b, respectively, with epoxy or resin.

The calculated natural frequencies for stacked bender bar 200 shown in FIG. 8 are given in Table 2. Modes 1, 5, and 10 correspond to three symmetric mode shapes, which are illustrated in FIGS. 9A, 9B, and 9C, respectively. FIG. 10 illustrates the harmonic displacement in Z direction of bender bar 200 illustrated in FIG. 8 compared to those of bender bar 100 illustrated in FIG. 5.

TABLE 2 Mode 1 2 3 4 5 6 7 Freq 367.53 856.3 944.01 1590.7 3463.9 4567.8 4869 (Hz) Mode 8 9 10 11 12 13 14 Freq 5518.1 6016.1 6593.3 6738.6 9016.2 9054.3 9334 (Hz)

FIGS. 9A, 9B, and 9C show Symmetric bending modes of the example of bender bar 200 illustrated in FIG. 8. In accordance with Table 2, FIG. 9A illustrates mode 1 at 367.53 Hz, FIG. 9B illustrates mode 5 at 3463.9 Hz, and FIG. 9C illustrates mode 10 at 6593.3 Hz. These modes represent the lower frequency symmetric modes of bender bar 200, with mode 1 of bender bar 200 having 0 nodes illustrated in FIG. 9A, with mode 5 of bender bar 200 having 2 nodes illustrated in FIG. 9B, and with mode 10 of bender bar 200 having 4 nodes illustrated in FIG. 9C.

FIG. 10 illustrates the harmonic displacement in the Z-direction of the center point of the example bender bar 200 illustrated in FIG. 8 in comparison with bender bar 100 as illustrated in FIG. 5. Peaks 702, 704, and 706 corresponding to modes 1, 5, and 9, respectively, of bender bar 100 of FIG. 5 are illustrated. Peaks 1002, 1004, and 1006 corresponding to modes 1, 5, and 10, respectively, of bender bar 200 of FIG. 8 are illustrated. As shown in FIG. 10 and Tables 1 and 2, peaks 1004 and 1006 are shifted to higher frequencies while peak 1002 is shifted to a slightly lower frequency.

The stacked bender bar computed results illustrated in FIG. 10 show that the addition of the additional ferroelectric element 204 a and 204 b, which provides extra mass, did not reduce the frequency response, and instead adjusted the frequency of most of the symmetric modes to higher frequency. The frequency (f) of the modes of a mechanical system is governed by the relation:

$\begin{matrix} {\left. f\longrightarrow\sqrt{\frac{k}{m}} \right.,} & {{Eq}.\mspace{14mu}(1)} \end{matrix}$

where k=stiffness and m=mass. If the mass m increases compared to stiffness k, the frequency will be lower. However, as shown in FIG. 10, it seems the stiffness k is increasing more than the mass m, resulting in an increase in frequency. Therefore, embodiments of the disclosure as illustrated in FIGS. 2A, 2B, 2C, and 2D and in FIG. 8 can be utilized to shift operating frequencies of bender bars to higher frequencies.

FIGS. 11A, 11B, and 11C illustrate a bender bar transducer 1100 according to some embodiments of the present disclosure that may lower the frequency and may provide more power. As shown in FIG. 11, transducer 1100 includes an inert element 1102. Transducer 1100 also includes pairs of ferroelectric elements, ferroelectric elements 1104 a and 1104 b and ferroelectric elements 1106 a and 1106 b, bonded to inert element 1102 such that there are gaps 1108 a and 1108 b at the center point of inert element 1102. Bender bar 1100 is similar to bender bar 100, except that the stiffness k is reduced by stripping off portions of ferroelectric elements 104 a and 104 b from the middle of bender bar 100 to form ferroelectric elements 1104 a and 1104 b and 1106 a and 1106 b.

In a particular example as shown in FIG. 11C, inert element inert element 1102 is a brass plate of thickness 0.125 inch, length 7.7 inch, and width 1.1 inch. Ferroelectric elements 1104 a and 1104 b and ferroelectric elements 1106 a and 1106 b are PZT crystal (C5400 or PZT-4 purchased from Channel Industries or Piezo Technologies). Each of ferroelectric elements 1104 a and 1104 b and ferroelectric elements 1106 a and 1106 b has a thickness of 0.125 inch, width of 1.0 inch, and length of 2 inch. Ferroelectric element 1104 a and ferroelectric element 1106 a are positioned symmetrically on one side of inert element 1102 such that a 0.063 inch gap is formed along a center line of inert element 1102. Similarly, ferroelectric element 1104 b and 1106 b are positioned symmetrically on the other side of inert element 1102 such that a 0.063 inch gap is formed on the center line of inert element 1102. Ferroelectric elements 1104 a and 1104 b and ferroelectric elements 1106 a and 1106 b are bonded to inert element 1102 with an epoxy or resin.

The calculated natural frequencies of bender bar 1100 as illustrated in FIG. 11C with the dimensions described above are shown in Table 3. FIGS. 12A, 12B, and 12C illustrate the three symmetric mode shapes indicated by mode 1 at 352.39 Hz, mode 5 at 2035.7 Hz, and mode 9 at 5654.2 Hz in Table 3. As discussed above, the displacements shown in FIGS. 12A, 12B, and 12C are not to scale.

TABLE 3 Mode 1 2 3 4 5 6 7 Freq 352.39 967.65 1019.1 1732.8 2035.7 4614.2 4678.2 (Hz) Mode 8 9 10 11 12 13 14 Freq 4732.7 5654.2 6325.6 6778.7 7628.5 8204.0 8967.9 (Hz)

FIG. 13 illustrates the harmonic displacement in Z-direction of the center point of bender bar 1100 illustrated by FIG. 11C in comparison with the harmonic displacement bender bar 100 as illustrated by FIG. 5. As shown in FIG. 13, peak 702 corresponds to mode 1 of bender bar 100, peak 704 corresponds to mode 5 of bender bar 100, and peak 706 corresponds to mode 9 of bender bar 100. The mode frequencies for bender bar 100 are illustrated in Table 1. In comparison, mode 1 of bender bar 1100 results in peak 1302, mode 5 of bender bar 1100 results in peak 1304, and mode 9 of bender bar 1100 results in peak 1306. From these calculated results, it is clear that the split bender bar 1100 shifts lower the natural frequency of the symmetric modes of bender bar 1100 compared to that of the un-split bender bar 100.

FIGS. 14A, 14B, 14C, and 14D illustrate a stacked and split embodiment bender bar 1400. The example embodiment illustrated in FIG. 14A, for example, includes inert element 1410 with multiple layers of ferroelectric elements on each side, arranged such that gaps 1420 a and 1420 b are formed in the stacked ferroelectric elements at a center line of bender bar 1400. Any number of layers can be utilized. The particular example illustrated in FIG. 14A should not be considered limiting.

As shown in FIG. 14A, ferroelectric elements 1402 a and 1402 b and ferroelectric elements 1412 a and 1412 b are bonded to inert element 1410 in such a fashion that a gap 1420 a is formed between ferroelectric element 1402 a and 1412 a and a gap 1420 b is formed between ferroelectric element 1402 b and 1412 b. Ferroelectric element 1402 a and 1402 b and ferroelectric element 1412 a and 1412 b can all be of the same size and shape and are positioned such that loading of inert element 1410 is symmetrical around the center line at gap 1420 b and 1420 a.

Similarly, ferroelectric elements 1404 a is bonded on ferroelectric element 1402 a, ferroelectric element 1404 b is bonded on ferroelectric element 1402 b, ferroelectric element 1414 a is bonded on ferroelectric element 1412 a, and ferroelectric element 1414 b is bonded on ferroelectric element 1412 b so that the loading is symmetrical and that the gaps 1420 a and 1420 b are maintained. Similarly, ferroelectric element 1406 a is bonded on ferroelectric element 1404 a, ferroelectric element 1416 a is bonded on ferroelectric element 1414 a, ferroelectric element 1406 b is bonded on ferroelectric element 1404 b and ferroelectric element 1416 b is bonded on ferroelectric element 1414 b. Additionally, ferroelectric element 1408 a is bonded on ferroelectric element 1406 a, ferroelectric element 1418 a is bonded on ferroelectric element 1416 a, ferroelectric element 1408 b is bonded on ferroelectric element 1406 b, and ferroelectric element 1418 b is bonded on ferroelectric element 1416 b. As a consequence, stacks of ferroelectric element are formed on inert element 1410 in such a way that gaps 1420 a and 1420 b are formed between the ferroelectric elements. In some embodiments, this arrangement adds to the mass loading m of bender bar 1400, it does not increase the stiffness k, resulting in lowered operating frequencies.

FIG. 14B illustrates some embodiments of bender bar 1400 as illustrated in FIG. 14A, where each of ferroelectric elements 1402 a, 1404 a, 1406 a, and 1408 a and ferroelectric elements 1412 a, 1414 a, 1416 a, and 1418 a (and correspondingly 1402 b, 1404 b, 1406 b, and 1408 b and ferroelectric elements 1412 b, 1414 b, 1416 b, and 1418 b) are rectangular and have the same width, but differing lengths. Each layer may also have a different thickness.

FIG. 14C illustrates some embodiments where each of ferroelectric elements 1402 a, 1404 a, 1406 a, and 1408 a and ferroelectric elements 1412 a, 1414 a, 1416 a, and 1418 a (and correspondingly 1402 b, 1404 b, 1406 b, and 1408 b and ferroelectric elements 1412 b, 1414 b, 1416 b, and 1418 b) are rectangular and have differing widths and lengths. Again, thicknesses may differ between layers.

FIG. 14D illustrates some embodiments where each of ferroelectric elements 1402 a and 1412 a (and correspondingly 1402 b and 1412 b) are rectangular and ferroelectric elements 1404 a, 1406 a, and 1408 a and ferroelectric elements 1412 a, 1414 a, 1416 a, and 1418 a (and correspondingly 1404 b, 1406 b, and 1408 b and ferroelectric elements 1414 b, 1416 b, and 1418 b) are semi-elliptical slabs and of differing major and minor axis lengths. In such case, ferroelectric elements 1404 a and 1414 a together form a whole ellipse with a cut in the center at gap 1420 a; ferroelectric elements 1406 a and 1416 a form a whole ellipse with a cut in the center at gap 1420 a; and ferroelectric elements 1408 a and 1418 a form a whole ellipse with a cut in the center at gap 1420 a. Again, thicknesses may differ between layers.

FIG. 15 illustrates a particular example of bender bar 1400. The particular example of bender bar 1400 of FIG. 15 includes ferroelectric elements 1402 a and 1402 b, ferroelectric elements 1404 a and 1404 b, ferroelectric elements 1412 a and 1412 b, and ferroelectric elements 1414 a and 1414 b to form a two-layered stack. The results of calculations of the natural frequencies of such a system are provided in Table 4. In that calculation, Inert element 1410 and ferroelectric elements 1402 a and 1402 b and ferroelectric elements 1412 a and 1412 b are the same elements and dimensions as inert element 1100 and ferroelectric elements 1104 a and 1104 b and ferroelectric elements 1106 a and 1106 b illustrated in FIG. 5. In other words, inert element 1410 is a brass plate of thickness 0.125 inch, length 7.7 inch, and width 1.1 inch. Ferroelectric elements 1402 a, 1402 b, 1404 a, 1404 b, 1412 a, 1412 b, 1414 a, and 1414 b are PZT crystal (C5400 or PZT-4, which can be purchased, for example, from Channel Industries or Piezo Technologies).

Each of Ferroelectric elements 1402 a and 1402 b and ferroelectric elements 1412 a and 1412 b has a thickness of 0.125 inch, width of 1.0 inch, and length of 2 inches. Ferroelectric elements 1402 a and 1412 a and ferroelectric elements 1402 b and 1412 b are positioned to form gap 1420 a and 1420 b, respectively, of width 0.03 inch. Ferroelectric elements 1402 a and 1402 b and ferroelectric elements 1412 a and 1412 b are bonded to inert element 210 by an epoxy or resin. Ferroelectric elements 1404 a and 1404 b and ferroelectric elements 1414 a and 1414 b have thickness of 0.125 inch, width of 1.0 inch, and length of 1 inch. Ferroelectric elements 1404 a and 1414 a and ferroelectric elements 1404 b and 1414 b are positioned to form gaps 1420 a and 1420 b, respectively, of width 0.03 inch. Ferroelectric elements 1404 a and 1404 b are bonded to ferroelectric elements 1402 a and 1402 b, respectively, by epoxy or resin. Ferroelectric elements 1414 a and 1414 b are bonded to ferroelectric elements 1412 a and 1412 b, respectively, by epoxy or resin.

The results of the calculation on bender bar 1400 as illustrated in FIG. 15 (e.g., a stacked and split bender bar) are shown in Table 4. Illustrates of the first three symmetric modes, modes 1, 5, and 8, are illustrated in FIGS. 16A, 16B, and 16C, respectively. FIG. 17 illustrates a comparison of the frequencies of modes 1, 5, and 8 of bender bar 1400 with those of bender bar 100 as illustrated in FIG. 5. As shown in FIG. 17, mode 1 at 321.08 Hz is illustrated as peak 1702, mode 5 at 2013.6 Hz is illustrated as peak 1704, and mode 8 at 5500.7 Hz is illustrated as peak 1706.

TABLE 4 No. 1 2 3 4 5 6 7 Freq 321.08 860.71 942.09 1527.0 2013.6 4526.3 4862.2 (Hz) No. 8 9 10 11 12 13 14 Freq 5500.7 5549.3 5765.5 6741.5 8305.7 8670.3 8984.4 (Hz)

FIG. 18 illustrates a narrow band pulse for driving ferroelectric elements with different center frequency. The main objective is to study the displacement of the mid-point of the bender element. Note that, since there is no loading of the system, the response would be dominated by the harmonic displacements as described in static models discussed above. To show the effects of the multiple driving pulse shapes in different PZT type ferroelectric elements, we use 1000 Hz and 750 Hz narrow pulses with different voltages applied to the stacked elements. The results are shown in the FIG. 19. As such, the waveform illustrated in FIG. 18 was applied to the ferroelectric elements of the bender bars in the above identified calculations.

FIG. 19 illustrates dynamic modeling results between driving stacked element with the same driving pulses 1902 with 1000 Hz center frequency and different driving pulses 1904 (1000 Hz pulse applied to the longer PZT element and 750 Hz to the shorter PZT element of bender bar 200 of FIG. 8). As shown in FIG. 19, plot (a) indicates a Time response, plot (b) indicates the Instantaneous frequency (note that there is a spike in the instantaneous frequency for the same driving pulse), and plot (c) indicates the frequency response.

The results indicated in FIG. 19 show that the two different driving pulse shapes change the output responses. Note that these results are used only for two stacked elements. Multiple elements with different driving pulses could produce even better preferred responses. In summary, the controlled driving voltages and pulse shapes with multiple PZT elements could provide a desired response that is proposed in this disclosure.

FIGS. 20A and 20B are sectional and top-down views, respectively, of yet another illustrative embodiment of the present disclosure wherein an acoustic transducer (bender bar, for example) includes a ferroelectric actuator that is designed to optimize a specific predetermined deflection mode shape of the acoustic transducer. In this embodiment, transducer 2000 includes an inert element 2010 mounted to mounts 2006 a,b in a clamped-clamped fashion. Ferroelectric actuation elements 2004 a and 2004 b are mounted on both sides of inert element 2010. In alternative embodiments, however, only one shaped ferroelectric actuation element 2004 may be mounted on one side of inert element 2010. As previously described herein, ferroelectric actuation elements 2004 a,b are slabs of matter mounted on both sides of inert element 2010. Although not shown, ferroelectric actuation elements 2004 a,b are electrically coupled to suitable driver circuit electronics. As described therein, this illustrative embodiment of transducer 100 provides a bi-polar acoustic wave as it is driven by suitable electronics.

As shown in FIGS. 20A-B, ferroelectric actuation elements 2004 a,b are designed to substantially couple with a specific and predetermined deflection mode shape of transducer 2000 such as, for example, a bender bar. By matching the shape of ferroelectric actuation elements 2004 a,b to the mode shape of transducer 2000, electrical energy is more efficiently converted into mechanical energy. With modal shaping, ferroelectric actuation elements 2004 a,b can transfer the electrical energy into the mechanical modes that efficiently radiate acoustic energy and, thus, avoid modes that do not efficiently radiate acoustic energy.

Accordingly, transducer 2000 accomplishes a desired modal shaping by utilizing shaped ferroelectric actuation elements 2004 a,b. As will be understood by those ordinarily skilled in the art having the benefit of this disclosure, a variety of methods such as, for example, finite element modeling (“FEM”), may be utilized to determine which shapes optimize which deflection modes. For example, the first mode of transducer 2000 can be determined to be a desired predetermined deflection mode. Therefore, ferroelectric actuation elements 2004 a,b can be cut to a shape, as determined using FEM for example, that most optimally couples to the first mode of transducer 2000. Accordingly, the energy from ferroelectric actuation elements 2004 a,b can be efficiently delivered into the first mode of transducer 2000 and not into higher modes. The result is a much flatter acoustic response, i.e., broadband, over the frequency range when actuated with a continuous single-frequency electrical input (as compared to conventional actuators).

FIG. 21 displays a plot of a frequency response comparison of a finite element analysis (“FEA”) simulation of a modally shaped transducer versus a conventional square actuator, according to an illustrative embodiment of the present disclosure. The modally shaped transducer, as described herein, is represented by solid line A, while the conventional transducer is represented by the dashed line B. The x-axis represents the excitation frequency in cycles per second (hertz) and the y-axis represents the relative sound pressure level.

As shown in FIG. 21, a coupled FEA analysis that includes the interaction of the transducer with wellbore fluid (drilling or completion fluid, for example) has been conducted on the shaped ferroelectric actuation elements. The calculated sound pressure at a distance six inches away is plotted for each line A and B. As seen, the frequency response of the shaped ferroelectric actuation elements (line A) is much flatter than the frequency response of a larger square actuator (line B). Moreover, the shaped actuator eliminates the “zeros” or minimums in acoustic output that are apparent with the square actuator.

FIGS. 22A-B illustrate an alternative embodiment of a transducer 2200 that utilizes weighted ferroelectric actuation elements to achieve modal shaping. For example, some bender bar transducers are designed to operate at the third length mode of vibration. As shown in FIG. 22A, three ferroelectric actuation elements 2204 a,b,c have been mounted on one side of inert element 2210. In alternative embodiments, however, ferroelectric actuation elements 2204 a,b,c may be mounted on both sides of inert element 2210. Nevertheless, transducer 2200 use of ferroelectric actuation elements 2204 a,b,c provides a better coupling to the third mode of inert element 2210, as shown in FIG. 22B which illustrates the third mode of vibration of inert element 2210. As shown, ferroelectric actuation elements 2204 a and 2204 c are polarized in a first positive direction, while ferroelectric actuation element 2204 b is polarized in a second negative direction opposite the first direction.

In alternative embodiments, however, ferroelectric actuation element 2204 b could be flipped over or electrically driven in the opposite direction. In yet other embodiments, the same effect of transducer 220 may be accomplished by changing the voltage applied to a given ferroelectric actuation element 2204 a,b,c, changing the amplitude of the voltages of the elements, or changing the amplitude of the polarity of the elements.

Unlike transducer 2200, many bender bars have the same poling of the ferroelectric ceramic actuators across the entire length of the beam (inert element). As a result, the electrical activation of the ceramics on the end of the bender bar would be working against the mode shape created by the actuation of the ceramic in the center. However, through use of a bender bar utilizing the features of modally shaped transducer 2200, a significantly larger acoustic output in a predetermined mode shape is obtained.

The illustrative modal shaping techniques described above allow the targeting of modes that are efficient acoustic radiators. As will be understood by those ordinarily skilled in the art having the benefit of this disclosure, the first and third modes are efficient acoustic dipole radiators, while the second and fourth modes are inefficient radiators. As is sometimes the case with conventional transducers, if the efficient acoustic modes are closely spaced in frequency to the inefficient modes, the resulting deflection shape may prominently feature the inefficient deflection shapes. However, through use of the modal shaping techniques described herein, desired deflection shapes can be forced into the shape of the efficient acoustic transmission.

In yet other illustrative embodiments of the present disclosure, modal shaping of the ferroelectric actuation elements also allows the targeting of efficient modes on round transducers. As will be understood by those ordinarily skilled in the art having the benefit of this disclosure, the first and sixth vibration modes are the most efficient acoustic radiators for bimorph or unimorph transducers. FIGS. 23A-D illustrate rounded modally shaped transducers at rest and in the third mode of vibration, according to certain illustrative embodiments of the present invention. In FIGS. 23A-D, a rounded transducer 2304 is mounted on one or both sides of rounded inert element 2310, and shown in a deflected position. Transducer 2304 has been cut using FEA, for example, to a shape that matches the third mode of vibration. As a result, the third mode of vibration of the bimorph is optimized, as shown in FIGS. 23C and D.

FIGS. 23A and 23C reflect illustrative modes of vibration for discs, which have the transducers divided in a circular manner. FIG. 23B shows the transducer in its lowest circular-nodal mode (0,1); and FIG. 23D shows it in the next circular-nodal mode (0,2). Note these are both deflected vibrational modes in one direction. The bimorph would be flat in its un-deformed, stress-free state, which is not shown in the figures. Also, a Unimorph is not shown in these figures, which would have the active element only on one side, but would perform in a similar identical manner, though less symmetrically.

The illustrative embodiments described herein may be utilized in a variety of applications including, for example, downhole applications. As such, the transducers may be embodied as bender bars utilized in downhole logging, and deployed along wirelines, drilling assemblies (LWD, for example), etc. When utilized as a bender bar, the transducers may be utilized as a transmitter or receiver, to thereby generate or receive acoustic radiation which propagates through the wellbore fluid. FIGS. 24A-B illustrate acoustic transducers utilized in a drilling and wireline application, respectively, according to illustrative embodiments of the present disclosure.

FIG. 24A illustrates a drilling platform 2 equipped with a derrick 4 that supports a hoist 6 for raising and lowering a drill string 8 through various formations 19. Hoist 6 suspends a top drive 11 suitable for rotating drill string 8 and lowering it through well head 13. Connected to the lower end of drill string 8 is a drill bit 15. As drill bit 15 rotates, it creates a wellbore 17 that passes through various formations 19. Although depicted as oriented in a vertical direction, the wellbore 17 can be oriented at other angles, including horizontal to the surface, and curvatures (e.g. “U” shaped, etc.) A pump 21 circulates drilling fluid through a supply pipe 22 to top drive 11, down through the interior of drill string 8, through orifices in drill bit 15, back to the surface via the annulus around drill string 8, and into a retention pit 24. The drilling fluid transports cuttings from the wellbore 17 into pit 24 and aids in maintaining the integrity of wellbore 17. Various materials can be used for drilling fluid, including, but not limited to, a salt-water based conductive mud.

An acoustic logging tool 10 is integrated into the bottom-hole assembly near the bit 15. In one or more embodiments, logging tool 10 is an LWD tool utilizing a bender bar acoustic transducer as described herein. In other illustrative embodiments, logging tool 10 may be utilized in a wireline or tubing-convey logging application. Moreover, in certain illustrative embodiments, logging tool 10 may be adapted to perform logging operations in both open and cased hole environments.

Still referring to FIG. 24A, as drill bit 15 extends wellbore 17 through formations 19, logging tool 10 collects acoustic measurement signals relating to various formation properties, as well as the tool orientation and various other drilling conditions. In certain embodiments, logging tool 10 may take the form of a drill collar, i.e., a thick-walled tubular that provides weight and rigidity to aid the drilling process. A telemetry sub 28 may be included to transfer images and measurement data/signals to a surface receiver 30 and to receive commands from the surface. In some embodiments, telemetry sub 28 does not communicate with the surface, but rather stores logging data for later retrieval at the surface when the logging assembly is recovered.

Still referring to FIG. 24A, logging tool 10 includes a system control center (“SCC”), along with necessary processing/storage/communication circuitry, that is communicably coupled to one or more acoustic transmitters and/or receivers (not shown) utilized to acquire formation measurement signals reflecting formation parameters. In certain embodiments, once the measurement signals are acquired, the SCC calibrates the measurement signals and communicates the data back uphole and/or to other assembly components via telemetry sub 28. In an alternate embodiment, the system control center may be located at a remote location away from logging tool 10, such as the surface or in a different borehole, and performs the processing accordingly. These and other variations within the present disclosure will be readily apparent to those ordinarily skilled in the art having the benefit of this disclosure.

FIG. 24B illustrates an alternative embodiment of the present invention whereby an acoustic transducer is utilized in a wireline application. At various times during the drilling process, drill string 8 may be removed from the borehole as shown in FIG. 24B. Once drill string 8 has been removed, logging operations can be conducted using a wireline logging sonde 34, i.e., a probe suspended by a cable 41 having conductors for transporting power to the sonde 34 and telemetry from sonde 34 to the surface. The wireline logging sonde 34 includes an acoustic logging tool, that includes a transducer as described herein, to transmit and/or receiver acoustic forces. A logging facility 43 collects measurements from the logging sonde 34, and includes a computer system 45 for processing and storing the measurements gathered by the transmitter/receivers.

The modal shaping features of the illustrative embodiments may be combined with any of the other embodiments described herein. For example, the bender bar transducer 200 of FIGS. 2A-2D and 3 may include one or more shaped ferroelectric actuation elements 2004, the weighted ferroelectric actuation elements 2204 a,b,c, and/or the rounded modally shaped transducers of FIGS. 23A-D. In another example, bender bar transducer 1100 of FIGS. 11A and 11B may also include one or more shaped ferroelectric actuation elements 2004, the weighted ferroelectric actuation elements 2204 a,b,c, and/or the rounded modally shaped transducers of FIGS. 23A-D.

Through use of the illustrative embodiments of the present disclosure, bender bars are improved in a number of ways. First, for example, a larger acoustic output (increased pressure) is provided. Second, since lower voltages are needed, smaller electrical and feed-through connectors may be utilized. Third, an acoustic output with a wider frequency band (i.e., broadband signal) may be produced. As a result, the bender bar has a flatter frequency response which allows for sweeping of a broader acoustic transmission frequency. Fourth, a more consistent acoustic output is provided, all while maintaining a high modal purity (large dipole/monopole & dipole/quadrupole ratios, for example).

Embodiments described herein further relate to any one or more of the following paragraphs:

1. An acoustic transducer for use in a wellbore, the acoustic transducer comprising an inert element; and a ferroelectric actuation element coupled to the inert element to thereby produce acoustic forces that propagate through fluid within the wellbore, wherein the ferroelectric actuation element is configured to substantially couple with a predetermined mode shape of the acoustic transducer.

2. An acoustic transducer as defined in paragraph 1, wherein the acoustic transducer is a bender bar.

3. An acoustic transducer as defined in paragraphs 1 or 2, wherein the bender bar is utilized as a transmitter.

4. An acoustic transducer as defined in any of paragraphs 1-3, wherein the ferroelectric actuation element has a shape that corresponds to the predefined mode shape of the acoustic transducer.

5. An acoustic transducer as defined in any of paragraphs 1-4, wherein the ferroelectric actuation element comprises weighted ferroelectric actuation elements.

6. An acoustic transducer as defined in any of paragraphs 1-5, wherein the weighted ferroelectric actuation elements comprise: a first ferroelectric actuation element polarized in a first direction; and a second ferroelectric actuation element polarized in a second direction opposite the first direction, wherein the second ferroelectric actuation element is proximate the first ferroelectric actuation element.

7. An acoustic transducer as defined in any of paragraphs 1-6, wherein the weighted ferroelectric actuation elements further comprise a third ferroelectric actuation element polarized in the first direction, and wherein the second ferroelectric actuation element is positioned between the first and third ferroelectric actuation elements.

8. An acoustic transducer as defined in any of paragraphs 1-7, wherein the fluid along the wellbore is a drilling or completion fluid.

9. An acoustic transducer as defined in any of paragraphs 1-8, wherein the acoustic forces are dipole acoustic forces.

10. An acoustic transducer as defined in any of paragraphs 1-9, wherein the acoustic transducer is a rounded modally shaped transducer.

11. A method for performing a wellbore operation utilizing an acoustic transducer as defined in any of any of paragraphs 1-10, the method comprising deploying the acoustic transducer into the wellbore; using the ferroelectric actuation element, transferring electrical energy into a mechanical mode shape of the acoustic transducer that efficiently radiates acoustic energy; and radiating the acoustic energy through fluid of the wellbore.

12. A method as defined in paragraph 11, further comprising avoiding those mechanical mode shapes that do not efficiently radiate the acoustic energy.

13. A method as defined in paragraphs 11 or 12, wherein the wellbore operation is a wireline or logging-while-drilling operation.

14. A method of manufacturing an acoustic transducer, comprising: providing an inert element; providing a ferroelectric actuation element; configuring the ferroelectric actuation element to substantially couple with a predetermined mode shape of the acoustic transducer; and coupling the ferroelectric actuation element to the inert element.

15. A method as defined in paragraph 14, wherein the acoustic transducer produces acoustic forces that propagate through fluid within a wellbore.

16. A method as defined in paragraphs 14 or 15, wherein the acoustic transducer is provided as a bender bar.

17. A method as defined in any of paragraphs 14-16, wherein the bender bar is provided as a transmitter.

18. A method as defined in any of paragraphs 14-17, wherein configuring the ferroelectric actuation element further comprises shaping the ferroelectric actuation element to correspond to the predefined mode shape of the acoustic transducer.

19. A method as defined in any of paragraphs 14-18, wherein configuring the ferroelectric actuation element further comprises providing the ferroelectric actuation element as weighted ferroelectric actuation elements.

20. A method as defined in any of paragraphs 14-19, wherein providing the ferroelectric actuation element as weighted ferroelectric actuation elements further comprises: providing a first ferroelectric actuation element polarized in a first direction; and providing a second ferroelectric actuation element polarized in a second direction opposite the first direction, wherein the second ferroelectric actuation element is positioned proximate the first ferroelectric actuation element.

21. A method as defined in any of paragraphs 14-20, further comprising providing a third ferroelectric actuation element polarized in the first direction, wherein the second ferroelectric actuation element is positioned between the first and third ferroelectric actuation elements.

Although various embodiments and methodologies have been shown and described, the disclosure is not limited to such embodiments and methodologies and will be understood to include all modifications and variations as would be apparent to one skilled in the art. Therefore, it should be understood that the disclosure is not intended to be limited to the particular forms disclosed. Rather, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the disclosure as defined by the appended claims. 

What is claimed is:
 1. An acoustic transducer for use in a wellbore, the acoustic transducer comprising: an inert element; and a ferroelectric actuation element coupled to the inert element to thereby produce acoustic forces that propagate through fluid within the wellbore, wherein the acoustic transducer was manufactured using a method comprising: coupling driver circuitry to the ferroelectric actuation element; selecting a mode shape of vibration of the acoustic transducer; determining a geometric shape of the ferroelectric actuation element that, when driven by the driver circuitry, results in the ferroelectric actuation element causing the acoustic transducer to vibrate in the selected mode shape of vibration; shaping the ferroelectric actuation element to match the geometric shape, thereby configuring the ferroelectric actuation element to couple with the selected mode shape of vibration of the acoustic transducer; and coupling the ferroelectric actuation element to the inert element.
 2. An acoustic transducer as defined in claim 1, wherein the acoustic transducer is a bender bar.
 3. An acoustic transducer as defined in claim 2, wherein the bender bar is utilized as a transmitter.
 4. An acoustic transducer as defined in claim 1, wherein the ferroelectric actuation element comprises weighted ferroelectric actuation elements.
 5. An acoustic transducer as defined in claim 4, wherein the weighted ferroelectric actuation elements comprise: a first ferroelectric actuation element polarized in a first direction; and a second ferroelectric actuation element polarized in a second direction opposite the first direction, wherein the second ferroelectric actuation element is proximate the first ferroelectric actuation element.
 6. An acoustic transducer as defined in claim 5, wherein the weighted ferroelectric actuation elements further comprise a third ferroelectric actuation element polarized in the first direction, and wherein the second ferroelectric actuation element is positioned between the first and third ferroelectric actuation elements.
 7. An acoustic transducer as defined in claim 1, wherein the fluid along the wellbore is a drilling or completion fluid.
 8. An acoustic transducer as defined in claim 1, wherein the acoustic forces are dipole acoustic forces.
 9. An acoustic transducer as defined in claim 1, wherein the acoustic transducer is a rounded modally shaped transducer.
 10. A method for performing a wellbore operation utilizing an acoustic transducer as defined in any of claims 1-9, the method comprising: deploying the acoustic transducer into the wellbore; using the ferroelectric actuation element, transferring electrical energy into a mechanical mode shape of the acoustic transducer that efficiently radiates acoustic energy; and radiating the acoustic energy through fluid of the wellbore.
 11. A method as defined in claim 10, further comprising avoiding those mechanical mode shapes that do not efficiently radiate the acoustic energy.
 12. A method as defined in claim 10, wherein the wellbore operation is a wireline or logging-while-drilling operation.
 13. A method of manufacturing an acoustic transducer, comprising: providing an inert element; providing a ferroelectric actuation element; coupling driver circuitry to the ferroelectric actuation element; selecting a mode shape of vibration of the acoustic transducer; determining a geometric shape of the ferroelectric actuation element that, when driven by the driver circuitry, results in the ferroelectric actuation element causing the acoustic transducer to vibrate in the selected mode shape of vibration; shaping the ferroelectric actuation element to match the geometric shape, thereby configuring the ferroelectric actuation element to couple with the selected mode shape of vibration of the acoustic transducer; and coupling the ferroelectric actuation element to the inert element.
 14. A method as defined in claim 13, wherein the acoustic transducer produces acoustic forces that propagate through fluid within a wellbore.
 15. A method as defined in claim 13, wherein the acoustic transducer is provided as a bender bar.
 16. A method as defined in claim 15, wherein the bender bar is provided as a transmitter.
 17. A method as defined in claim 13, wherein configuring the ferroelectric actuation element further comprises providing the ferroelectric actuation element as weighted ferroelectric actuation elements.
 18. A method as defined in claim 17, wherein providing the ferroelectric actuation element as weighted ferroelectric actuation elements further comprises: providing a first ferroelectric actuation element polarized in a first direction; and providing a second ferroelectric actuation element polarized in a second direction opposite the first direction, wherein the second ferroelectric actuation element is positioned proximate the first ferroelectric actuation element.
 19. A method as defined in claim 18, further comprising providing a third ferroelectric actuation element polarized in the first direction, wherein the second ferroelectric actuation element is positioned between the first and third ferroelectric actuation elements. 